"China doesn't pay much attention to what Trump says. It mainly pays attention to what Trump does," he said.

"We need to wait and see what he will do rather than what he said," echoed Lu Xiang, an expert in Sino-U.S. relations at the Chinese Academy of Social Sciences in Beijing.

In Russia, the Kremlin took a sharper line.

Speaking with journalists on Tuesday, a Kremlin spokesman criticized the new national security plan for its "imperial character" and said it incorrectly painted Russia as a threat to the ­national security of the United States.

"The clearly imperial character of the document, the clear lack of desire to reject a unipolar world, and a reluctance to accept a multipolar world," said Dmitry Peskov, President Vladimir Putin's personal spokesman, when asked what parts of the speech concerned the Kremlin.

"Of course, we cannot agree with the attitude, which defines our country as a threat to the United States' security," he said, in remarks translated by the Interfax news service.

The gap between what Trump has said on China and what he has done is the source of much debate here — and Monday's speech did little to change that.

As a candidate, Trump regularly lashed out at China, even accusing the country of "raping" the United States. As president, he has veered between tough talk — on North Korea, for instance — and sweet talk — mostly reserved for China's "highly respected" authoritarian leader, Xi Jinping.

Over the weekend, reports circulated that Trump's speech and strategy would treat China as a competitor and call out the country's "economic aggression." But only the first part made the cut.

In his remarks, Trump called China and Russia "rival powers" that "seek to challenge American influence, values and wealth."

He went on to say the United States will "attempt to build a great partnership with those and other countries, but in a manner that always protects our national interest."

The strategy document offered a bit more detail. "China and Russia challenge American power, influence, and interests, ­attempting to erode American ­security and prosperity," it reads.

"They are determined to make economies less free and less fair, to grow their militaries, and to control information and data to repress their societies and expand their influence."

Language such as "rival" is part of a White House push to frame China as a "strategic competitor" instead of a "strategic partner" — a rhetorical shift that did not go unnoticed by the Chinese.

"Cooperation is the only correct choice for China and the United States," Hua Chunying, a spokeswoman for the Chinese Foreign Ministry, said at a regular news briefing on Tuesday. "We urge the U.S. side to stop distorting China's strategic intentions."

The China Daily editorial noted that President George W. Bush described China as a strategic competitor when he came to power, but over time "came to see China as a 'responsible stakeholder,' paving the way for years of stability in Sino-U.S. relations."

Scott Kennedy, director of the project on Chinese business at the Center for Strategic and International Studies in Washington, said the "competition" framing would irk Beijing, but not as much as it used to.

"The Chinese leadership has already decided that the U.S. is a strategic rival," he said.

Their thinking, in terms of the word "partnership," is, "You might say it, and we might say it, but we won't necessarily believe it," Kennedy said.

The text of the strategy document offered some clues to how the Trump administration sees the rivalry. It briefly mentions, for instance, Chinese military advancements and the fact that Beijing uses investment in the developing world to cultivate influence.

It also notes that every year, "competitors such as China steal U.S. intellectual property valued at hundreds of billions."

The document says the United States "must defend our National Security Innovation Base (NSIB) against competitors" but does not spell out what policy changes, if any, are to come.

For more than a decade, Putin has called for a new international balance of power with multiple poles of influence including Moscow. The Kremlin has regularly complained of U.S. hegemony in international politics, a criticism that was most forcefully laid out in a 2007 speech given by Putin at the Munich Security Conference.

"No one feels safe!" Putin said at the time. "Because no one can feel that international law is like a stone wall that will protect them."

But to Chinese experts, the lack of specificity on Trump's part Monday was generally taken as a sign of U.S. weakness.

Victor Gao, a Beijing-based current affairs commentator and former translator for Deng Xiaoping, said the idea that U.S. global leadership cannot be challenged now looks "negotiable."

"As the top dog, the number one country in the world, you should make an effort to protect your world leader status," he said.

"If another country has better growth and a better developmental strategy, you should be humble and learn from them rather than repeatedly saying, 'You should not challenge me.' "